Question: Simplify the following expression: $ n = \dfrac{5}{9} - \dfrac{-6x - 2}{-10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{5}{9} \times \dfrac{-10}{-10} = \dfrac{-50}{-90} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6x - 2}{-10} \times \dfrac{9}{9} = \dfrac{-54x - 18}{-90} $ Therefore $ n = \dfrac{-50}{-90} - \dfrac{-54x - 18}{-90} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-50 - (-54x - 18) }{-90} $ Distribute the negative sign: $n = \dfrac{-50 + 54x + 18}{-90}$ $n = \dfrac{54x - 32}{-90}$ Simplify the expression by dividing the numerator and denominator by -2: $n = \dfrac{-27x + 16}{45}$